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In recent years, fantasy baseball has seen an explosion in popularity. Major League Baseball, with its long, storied history and the enormous quantity of data available, naturally lends itself to the modern-day recreational activity known as fantasy baseball. Fantasy baseball is a game in which participants manage an imaginary roster of real players and compete against one another using those players' real-life statistics to score points. Early forms of fantasy baseball began in the early 1960s, but beginning in the 1990s, the sport was revolutionized due to the advent of powerful computers and the Internet. The data used in this project come from an actual fantasy baseball league which uses a head-to-head, points-based scoring system. The data consist of the weekly point totals that were accumulated over the first three-fourths of the 2011 regular season by the top 110 hitters and top 70 pitchers in Major League Baseball. The purpose of this project is analyze the relative value of pitchers versus hitters in this league using hierarchical Bayesian models. Three models will be compared, one which differentiates between hitters and pitchers, another which also differentiates between starting pitchers and relief pitchers, and a third which makes no distinction whatsoever between hitters and pitchers. The models will be compared using the deviance information criterion (DIC). The best model will then be used to predict weekly point totals for the last fourth of the 2011 season. Posterior predictive densities will be compared to actual weekly scores.

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Despite the profound impact of deep learning across various domains, supervised model training critically depends on access to large, high-quality datasets, which are often challenging to identify. To address this, we introduce <b>H</b>ierarchical <b>B</b>ayesian <b>D</b>ataset <b>S</b>election (<b>HBDS</b>), the first dataset selection algorithm that utilizes hierarchical Bayesian modeling, designed for collaborative data-sharing ecosystems. The proposed method efficiently decomposes the contributions of dataset groups and individual datasets to local model performance using Bayesian updates with small data samples. Our experiments on two benchmark datasets demonstrate that HBDS not only offers a computationally lightweight solution but also enhances interpretability compared to existing data selection methods, by revealing deep insights into dataset interrelationships through learned posterior distributions. HBDS outperforms traditional non-hierarchical methods by correctly identifying all relevant datasets, achieving optimal accuracy with fewer computational steps, even when initial model accuracy is low. Specifically, HBDS surpasses its non-hierarchical counterpart by 1.8% on DIGIT-FIVE and 0.7% on DOMAINNET, on average. In settings with limited resources, HBDS achieves a 6.9% higher accuracy than its non-hierarchical counterpart. These results confirm HBDS's effectiveness in identifying datasets that improve the accuracy and efficiency of deep learning models when collaborative data utilization is essential. / Master of Science / Deep learning technologies have revolutionized many domains and applications, from voice recognition in smartphones to automated recommendations on streaming services. However, the success of these technologies heavily relies on having access to large and high-quality datasets. In many cases, selecting the right datasets can be a daunting challenge. To tackle this, we have developed a new method that can quickly figure out which datasets or groups of datasets contribute most to improving the performance of a model with only a small amount of data needed. Our tests prove that this method is not only effective and light on computation but also helps us understand better how different datasets relate to each other.

Student Number: 9811822T - MSc Dissertation - School of Computational and Applied Mathematics - Faculty of Science / This dissertation reviews population dynamic type models of viral infection and introduces some new models to describe strain competition and the infected cell lifecycle. Laboratory data from a recent clinical trial, tracking drug resistant virus in patients given a short course of monotherapy is comprehensively analysed, paying particular attention to reproducibility. A Bayesian framework is introduced, which facilitates the inference of model parameters from the clinical data. It appears that the rapid emergence of resistance is a challenge to popular unstructured models of viral infection, and this challenge is partly addressed. In particular, it appears that minimal ordinary differential equations, with their implicit exponential lifetime (constant hazard) distributions in all compartments, lack the short transient timescales observed clinically. Directions for future work, both in terms of obtaining more informative data, and developing more systematic approaches to model building, are identified.

This thesis develops a GIS-based Bayesian approach for area-wide traffic crash analysis. Five years of crash data from Houston, Texas, are analyzed using a geographic information system (GIS), and spatial-temporal patterns of relative crash risk are identified based on a hierarchical Bayesian approach. This Bayesian approach is used to filter the uncertainty in the data and identify and rank roadway segments with potentially high relative risks for crashes. The results provide a sound basis to take preventive actions to reduce the risks in these segments. To capture the real safety indications better, this thesis differentiates the risks in different directions of the roadways, disaggregates different road types, and utilizes GIS to analyze and visualize the spatial relative crash risks in 3-D views according to different temporal scales. Results demonstrate that the approach is effective in spatially smoothing the relative crash risks, eliminating the instability of estimates while maintaining real safety trends. The posterior risk maps show high-risk roadway segments in 3-D views, which is more reader friendly than the conventional 2-D views. The results are also useful for travelers to choose relatively safer routes.

This thesis develops a GIS-based Bayesian approach for area-wide traffic crash analysis. Five years of crash data from Houston, Texas, are analyzed using a geographic information system (GIS), and spatial-temporal patterns of relative crash risk are identified based on a hierarchical Bayesian approach. This Bayesian approach is used to filter the uncertainty in the data and identify and rank roadway segments with potentially high relative risks for crashes. The results provide a sound basis to take preventive actions to reduce the risks in these segments. To capture the real safety indications better, this thesis differentiates the risks in different directions of the roadways, disaggregates different road types, and utilizes GIS to analyze and visualize the spatial relative crash risks in 3-D views according to different temporal scales. Results demonstrate that the approach is effective in spatially smoothing the relative crash risks, eliminating the instability of estimates while maintaining real safety trends. The posterior risk maps show high-risk roadway segments in 3-D views, which is more reader friendly than the conventional 2-D views. The results are also useful for travelers to choose relatively safer routes.

Univariate hierarchical Bayes models are being vigorously researched for use in disease mapping, engineering, geology, and ecology. This dissertation shows how the models can also be used to build modelbased risk maps for areabased roadway tra&#64259;c crashes. Countylevel vehicle crash records and roadway data from Texas are used to illustrate the method. A potential extension that uses univariate hierarchical models to develop networkbased risk maps is also discussed. Several Bayesian multivariate spatial models for estimating the tra&#64259;c crash rates from di&#64256;erent types of crashes simultaneously are then developed. The speci&#64257;c class of spatial models considered is conditional autoregressive (CAR) model. The univariate CAR model is generalized for several multivariate cases. A general theorem for each case is provided to ensure that the posterior distribution is proper under improper and &#64258;at prior. The performance of various multivariate spatial models is compared using a Bayesian information criterion. The Markov chain Monte Carlo (MCMC) computational techniques are used for the model parameter estimation and statistical inference. These models are illustrated and compared again with the Texas crash data. There are many directions in which this study can be extended. This dissertation concludes with a short summary of this research and recommends several promising extensions.

Made available in DSpace on 2015-03-26T13:32:20Z (GMT). No. of bitstreams: 1 texto completo.pdf: 475570 bytes, checksum: 32a4377514ec0978d86cb9bc9fcb45f1 (MD5) Previous issue date: 2013-07-31 / A hierarchical Bayesian modeling was used to evaluate the influence of halothane gene and its interaction with sex on pig &#769;s growth curves. Under this approach, the parameters from growth models (Logistic, Gompertz and von Bertalanffy) were estimated jointly with the effects of halothane gene and sex. A total of 344 F2 (Commercial x Piau) animals were weighted at birth, 21, 42, 63, 77, 105 and 150 days in life. The Logistic model has presented the best fit based on DIC (Deviance Information Criterion). Thus, the samples from marginal posterior distributions for the differences between the parameters estimates of Logistic model have indicated that the maturity weight of males with heterozygous genotypes (HALNn) was superior to males with homozygous genotypes (HALNN). In order to realize a comparison with the traditional methodology, the frequentist approach based on two distinct steps also was used, but there was not identified significant differences between growth curve parameter estimates from each group (combinations of halothane genotypes and sex). / Para avaliar a influência do gene halotano sobre a curva de crescimento de suínos, bem como sua interação com o sexo do animal, foi proposta uma modelagem hierárquica Bayesiana. Nesta abordagem, os parâmetros dos modelos não-lineares de crescimento (Logístico, Gompertz e von Bertalanffy) foram estimados conjuntamente com os efeitos de sexo e genótipos do gene halotano. Foram utilizados 344 animais F2(Comercial x Piau) pesados ao nascer, aos 21, 42, 63, 77, 105 e 150 dias. O modelo Logístico foi aquele que apresentou melhor qualidade de ajuste por apresentar menor DIC (Deviance Information Criterion) que os demais. As amostras das distribuições marginais a posteriori para as diferenças entre as estimativas dos parâmetros do modelo Logístico indicaram que o peso dos machos à idade adulta com genótipo heterozigoto (HALNn) foi superior ao dos homozigotos (HALNN). A título de comparação, também foi considerada a abordagem frequentista tradicional baseada em dois passos distintos, a qual, por apresentar um menor poder de discernimento estatístico, não mostrou diferenças significativas.

Better understanding and prediction of tree growth is important because of the many ecosystem services provided by forests and the uncertainty surrounding how forests will respond to anthropogenic climate change. With the ultimate goal of improving models of forest dynamics, here we construct a statistical model that combines complementary data sources, tree-ring and forest inventory data. A Bayesian hierarchical model was used to gain inference on the effects of many factors on tree growth-individual tree size, climate, biophysical conditions, stand-level competitive environment, tree-level canopy status, and forest management treatments-using both diameter at breast height (dbh) and tree-ring data. The model consists of two multiple regression models, one each for the two data sources, linked via a constant of proportionality between coefficients that are found in parallel in the two regressions. This model was applied to a data set of similar to 130 increment cores and similar to 500 repeat measurements of dbh at a single site in the Jemez Mountains of north-central New Mexico, USA. The tree-ring data serve as the only source of information on how annual growth responds to climate variation, whereas both data types inform non-climatic effects on growth. Inferences from the model included positive effects on growth of seasonal precipitation, wetness index, and height ratio, and negative effects of dbh, seasonal temperature, southerly aspect and radiation, and plot basal area. Climatic effects inferred by the model were confirmed by a den-droclimatic analysis. Combining the two data sources substantially reduced uncertainty about non-climate fixed effects on radial increments. This demonstrates that forest inventory data measured on many trees, combined with tree-ring data developed for a small number of trees, can be used to quantify and parse multiple influences on absolute tree growth. We highlight the kinds of research questions that can be addressed by combining the high-resolution information on climate effects contained in tree rings with the rich tree-and stand-level information found in forest inventories, including projection of tree growth under future climate scenarios, carbon accounting, and investigation of management actions aimed at increasing forest resilience.